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Chapter 6: Q. 6 (page 409)

Questions T6.5 and T6.6 refer to the following setting. The weight of tomatoes chosen at random from a bin at the farmer鈥檚 market is a random variable with mean 渭=10ounces and standard deviation 蟽=1ounce. Suppose we pick four tomatoes at random from the bin and find their
total weight T.

T6.6. The random variableT has a standard deviation (in ounces) of
(a) 0.25.(b) 0.50.(c) 0.71. (d) 2(e) 4

Short Answer

Expert verified

The random variableT has a standard deviation of 2ounces. So, the option(d) is correct.

Step by step solution

01

Given information

The farmer鈥檚 market is a random variable with mean 渭=10ounces and standard deviation 蟽=1ounce.

02

Explanation

Let, X(one tomato) is 渭X=10and, 蟽X=1
Then,T is the random variable for the weight of four tomatoes:
T=X1+X2+X3+X4

And the properties mean and variance:

Note that Xand Yare independent:

渭X+Y=渭X+渭Y蟽2X+Y=蟽2X+蟽2Y

The mean and variance of Tis:

渭T=渭X1+X2+X3+X4=4渭X=4(10)=40

ounces.

蟽T2=蟽X1+X2+X3+X42=4蟽X2=412=4ounces2

The standard deviation is the square root of the variance:

蟽T=蟽T2=4=2ounces

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